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Homework answers / question archive / Suppose you observe the following direct spot quotations in New York and Toronto, respectively: 0

Suppose you observe the following direct spot quotations in New York and Toronto, respectively: 0

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Suppose you observe the following direct spot quotations in New York and Toronto, respectively: 0.8000-30 and 1.2500-70. What are the arbitrage profits per $1 million?

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Suppose you observe the following direct spot quotations in New York and Toronto, respectively: 0.8000-30 and 1.2500-70. What are the arbitrage profits per $1 million?

You can buy 1 Canadian dollar for $0.8030 and sell 1 Canadian dollar for $0.8000 in New York
This means that the bid rate for US dollar = CAD 1.2453 = 1/ .803
and the ask rate for US dollar is= CAD 1.2500 = 1/ .8 in New York

You can buy 1 US dollar for CAD 1.2570 and sell 1 US dollar for CAD 1.2500 in Toronto
This means that the bid rate for Canadian dollar = $0.7955 = 1/ 1.257
and the ask rate for Canadian dollar is= $0.8000 = 1/ 1.25 in Toronto

Since 1 US $ can be sold for CAD 1.2500 in Toronto ,
And 1 Canadian dollar will buy $0.8000 in New York ,
Therefore, CAD 1.2500 will purchase $1.0000 in New York , = 1.25 x 0.8
there is no arbitrage profit as you would get $1.0000 for every US $ invested

Alternatively
Buy 1 Canadian $ for $0.8030 in New York
Therefore 1 US $ will get CAD 1.2453 = 1/ .803 in New York
1 US $ can be purchased for CAD 1.2570 in Toronto
Therefore, CAD 1.2453 will purchase $0.9907 in Toronto

Thus there is no arbitrage profit

Amount invested= $1,000,000
Sell it to buy Canadian $ in Toronto
Selling price of US dollar in Toronto= CAD 1.2500
Amount of CAD purchased= CAD 1,250,000 =1000000 x 1.25

In New York purchase dollars
You can sell 1 Canadian dollar for $0.8000 in New York
Therefore CAD 1,250,000 will purchase $1,000,000 =1250000 x 0.8
Amount of US dollars purchased= $1,000,000 = Amount invested

Thus there is no arbitrage profit

Alternatively

Amount invested= $1,000,000
Sell it to buy Canadian $ in New York
Price of Canadian $ in New York= $0.8030
Amount of CAD purchased= CAD 1,245,330 =1000000 / 0.803

In Toronto sell Canadian dollars
1 US $ can be purchased for CAD 1.2570 in Toronto
Therefore CAD 1,245,330 will purchase $990,716 =1245330 / 1.257
Amount of US dollars purchased= $990,716 is less than the amount invested= $1,000,000

Thus there is no arbitrage profit.

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